Level 7

Shaun Cooper
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Shaun Cooper: Massey University, Institute of Natural and Mathematical Science

Chapter Chapter 7 in Ramanujan's Theta Functions, 2017, pp 423-466 from Springer

Abstract: Abstract We conduct an extensive study of the infinite products q − 2 ∕ 7 ∏ j = 1 ∞ ( 1 − q 7 j − 5 ) ( 1 − q 7 j − 2 ) ( 1 − q 7 j − 6 ) ( 1 − q 7 j − 1 ) , $$ q^{-2/7}\prod _{j=1}^{\infty }\frac{(1-q^{7j-5})(1-q^{7j-2})} {(1-q^{7j-6})(1-q^{7j-1})}, $$ − q − 1 ∕ 7 ∏ j = 1 ∞ ( 1 − q 7 j − 4 ) ( 1 − q 7 j − 3 ) ( 1 − q 7 j − 5 ) ( 1 − q 7 j − 2 ) , $$ -q^{-1/7}\prod _{j=1}^{\infty }\frac{(1-q^{7j-4})(1-q^{7j-3})} {(1-q^{7j-5})(1-q^{7j-2})}, $$ and q 3 ∕ 7 ∏ j = 1 ∞ ( 1 − q 7 j − 6 ) ( 1 − q 7 j − 1 ) ( 1 − q 7 j − 4 ) ( 1 − q 7 j − 3 ) $$ \displaystyle{q^{3/7}\prod _{ j=1}^{\infty }\frac{(1 - q^{7j-6})(1 - q^{7j-1})} {(1 - q^{7j-4})(1 - q^{7j-3})}} $$ and obtain results that are analogues of theorems in Chapters 5 and 6

Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-56172-1_8

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DOI: 10.1007/978-3-319-56172-1_8

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